Alpha

 Baysian analysis allows for joint probability, below:

If I add the two columns, I get back to the 'rain in the afternoon' set of probabiities.

If I add across rows, I return to the 'clouds in the morning' numbers. So what is likely to

happen on any given day: no cloud and no rain; cloud and no rain; cloud and rain; 

no cloud and rain. In that order...

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I can also ask a 'time-inverted' question. What is the probability of having experienced

cloud in the morning , given it is raining in the afternoon.

Alpha, here,  is used to produce a standard probability distribution that adds to 1!

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Just nstalled pomegranate, a probabilistic programming library for python.

Tomorrow...